Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
327 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| socle | C22 | C2×C4×D4 |
| prime radical | C23 | C2×#41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #500 | C4 | semidirect |
| 12. #499 | C4 | semidirect |
| 13. #499 | C4 | semidirect |
| 14. #498 | C4 | semidirect |
| 56. #97 | Q8 | semidirect |
| 63. C4×C8 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3160 | 2 |
| #2961 | 2 |
| #1995 | 2 |
| #1946 | 2 |
| #1945 | 2 |
| #1848 | 2 |
| #1773 | 2 |
| #1772 | 2 |
| #1726 | 2 |